A body of mass 300g is whirled in a horizontal circle by means of a 60cm long cord. If the cord can sustain a tension of 400N before, find the max. number of revolution per minute which the body can have
m omega^2 R = 400
0.300 w^2 (0.60) = 400
solve for w ( omega ) in radians/sec
then
w * 1 rev/2pi rad * 60 sec/min
= RPM
To find the maximum number of revolutions per minute (rpm) that the body can have, we need to consider the tension in the cord at maximum speed.
The tension in the cord can be calculated using the centripetal force formula:
Tension (T) = (mass of the body (m) × velocity^2 (v^2)) / radius (r)
Given:
Mass of the body (m) = 300g = 0.3kg
Radius (r) = 60cm = 0.6m
Maximum tension the cord can sustain (Tmax) = 400N
Rearranging the formula, we get:
v^2 = (T × r) / m
Now, let's solve for v:
v^2 = (400N × 0.6m) / 0.3kg
v^2 = 800N / 0.3kg
v^2 ≈ 2666.67 (approximately)
Now, let's solve for v:
v ≈ √(2666.67)
v ≈ 51.64 m/s (approximately)
Since the length of the cord remains constant, the distance traveled by the body in one revolution is equal to the circumference of the circle formed by the cord.
Circumference = 2πr = 2π × 0.6m ≈ 3.77m
To find the number of revolutions per minute, we need to convert the velocity from m/s to meters per minute:
Velocity (v) = 51.64 m/s
Velocity (v) ≈ 51.64 × 60 ≈ 3098.4 m/min (approximately)
Finally, divide the velocity in meters per minute by the distance per revolution to get the maximum number of revolutions per minute:
Number of revolutions per minute ≈ 3098.4m/min ÷ 3.77m
Number of revolutions per minute ≈ 821.54 revolutions per minute (approximately)
Therefore, the maximum number of revolutions per minute the body can have is approximately 821.54.